Indicator equivalence theorem for input rates and regional masses in multi-inlet steady-state systems with partially labeled input

Abstract

Bergner has derived for steady-state systems with fully labeled input: (a) the total input rate of traced substance, as the reciprocal of the time integral of specific activity per unit dose measured anywhere in the system; and (b) the mass of traced substance existing in any observable region within the system, as the product of the total input rate of traced substance and the time integral of the amount of tracer per unit dose in the region. These results are generalized to systems in which only part of the input rate is labeled. The relation between tracer sojourn time and mean transit time is derived. The parallelism between tracers (and traced substances) and foreign substances (and reference substances) is demonstrated. All results are derived from a relation, denoted the indicator equivalence theorem, between indicator (tracer or foreign substance) quantities measured in two experiments on the system: a finite injection experiment and a constant infusion experiment. This relation is derived by the convolution integral method which is applied between the input location and a local region of response inside the system. The indicator equivalence theorem permits an operational definition of any system parameter.